A young man stands in the crowded Bab el Louk produce market in downtown Cairo, cleaning the thorns off long-stemmed pink roses. He has just heard the inaugural speech of the new President, Hosni Mubarak.

''Did you ever hear the speeches of Abdel Nasser?'' he says dreamily to a customer. ''They were much more beautiful than Sadat's. I think Mubarak could be another Abdel Nasser.'' He scrapes off more thorns. ''In Abdel Nasser's time a kilo of meat cost 70 piastres. Now it costs (STR)3.50.'' (Or five times as much.)

An Egyptian intellectual sits in a hotel cafe, sipping a drink. He has been a forceful critic of Anwar Sadat. ''I think this man may be very good,'' he says of the new President, Hosni Mubarak.

''He never accepted gifts or bribes in the Army. He never showed favoritism. If he prays, he prays at home. It is between him and God, as with Abdel Nasser.

It is barely two weeks now since Hosni Mubarak formally assumed the Egyptian presidenci in the midst of one of Egypt's most profound political crises.

As the compact and taciturn former Air Force commander emerges from the shadows to replace the late Anwar Sadat, he has evoked in ordinary Egyptians, beset by the uncertainties that have followed Mr. Sadat's violent and unexpected death, the cherished memory of their strong and beloved leader, President Gamal Abdel Nasser.

''The people are comparing Mubarak to Nasser,'' says an Egyptian musician, a Coptic Christian. ''I think it comes from a deep need inside them. During Nasser's time there was security. In the past few years people have been afraid. You could walk on the street and get shot.''

The assassination of Mr. Mubarak's mentor, Anwar Sadat, at the hands of Muslim extremists from within the armed forces has shaken the Egyptian government to its roots.

The true strength of the armed Muslim fundamentalists that oppose the regime in Egypt is still a matter of conjecture. The Camp David peace process, upon which Mr. Sadat hinged Egyptian foreign policy and his special relationship with the United States, is threatened as a jittery and suspicious Israel weighs the painful final withdrawal from precious Sinai against an uncertain future.

A bellicose Libyan Col. Muammar Qaddafi laughs in triumph at Egypt's turmoil as a frightened Sudan clings to its northern ally for protection.

As Mr. Mubarak confronts the serious internal and external challenges that face him, he is also engaged in what one senior Egyptian calls ''the search for a constituency.''

For Mr. Mubarak to secure his new regime, many analysts in Cairo believe he must not only crush the Muslim fundamentalists who have challenged him, but must also offer Egyptians a positive alternative. This means offering popular appeal, mass symbols, and the call to patriotism and national sacrifice that will counter the heady message for the dispossessed masses of an idyllic Islamic state, and fill the current ideological vacuum in Egypt.

''I think people are projecting the image of Nasser onto Mubarak,'' suggested one veteran Western analyst, ''because there isn't anything else.''

The rise of Islamic societies in Egypt since the early '70s that now command a mass popular following, have fed on the variety of economic and social ills facing Egyptians, and the relatively free political atmosphere that allowed them to deliver their fiery sermons in various mosques around the country.

Advocating the return to a less corrupted, less Westernized Islamic past, intolerant of Egypt's Christian minority, condemning the Sadat regime for its peace with the Jewish enemy and secular practices, the tide of the Islamic societies had swelled to such alarming proportions by this year that Mr. Sadat had felt it necessary, a month before his death, to institute the most massive crackdown of his 11-year-rule. He imprisoned over 1,500 political opponents which included more than 1,000 Islamic fundamentalist leaders.Many Egyptians, Muslim and Christian, are very frightened of the Islamic groups. ''They will grow and grow,'' says one Egyptian journalist, a Muslim. ''We live in the decade of Islam.''One of Mr. Mubarak's first acts as President has been to move swiftly and decisively to crush the Islamic societies. A day after he was inaugurated as President on Oct. 14, news began to leak of a wave of unpublished mass arrests of fundamentalists that may have run into the thousands. But even that may not be enough.The government knows that Egypt's Islamic groups have traditionally shown amazing elasticity even under the most severe government repression. In 1954, President Nasser severely repressed the Muslim Brotherhood, which had tried to assassinate him. In 1965, he again uncovered several assassination plots and arrested many more. An investigation revealed the fundamentalists had penetrated the Army and police.Mr. Sadat also dealt harshly with bands of Muslim extremists in 1975, when they attacked the Egyptian military academy, and 1977, when they kidnapped and killed a former religious affairs minister. The leading members of both groups were executed, and many others imprisoned. Yet, in 1981, well-armed and fanatically committed Muslim extremists resurfaced and murdered Mr. Sadat, and almost succeeded in killing the entire Egyptian Cabinet.Echoes of Nasserism began with Mr. Mubarak's inaugural address, when he quoted a phrase from an early Nasser speech, promising to ''protect and not threaten, keep and not waste.'' Mr. Mubarak's clipped, direct speech, his modest living habits, predilection for hard work, and reputation for integrity have reinforced the Nasserist image, and provided a fresh change to Egyptians who had grown weary of Mr. Sadat's flamboyant and extravagant life style.The patriotic songs now being aired on Egyptian television come from the Nasser period. The new government's promise to fight corruption is a popular cause with both the political left and right, and the poor majority.The Egyptian media has already begun the first veiled criticisms of Sadat policies. One editorial in the semi-official al-Ahram hoped that ''the eagle,'' Mr. Mubarak, would be firmer with the Israelis.The other side of Mr. Mubarak's personality, the strict - some say almost brutal - disciplinarian, has reassured some Egyptians and worried others.The police and the military are now swarming over Cairo streets.''They are running the country, just like in '45,'' complained a taxi driver, stuck in traffic behind a military jeep filled with gun-toting soldiers.Soldiers and police now have the right to shoot agitators on sight; Egyptian universities are under heavy surveillance; and all public gatherings are banned under the year-long state of emergency. More than 150 leftists, many of whom have had nothing to do with recent events and actually fear and oppose the Islamic groups, have been arrested in the roundups of political dissidents.But most Egyptians are resigned to the current siege atmosphere for the foreseeable future.An elevator boy on downtown Kasr el-Nil Street tries to justify the government's latest moves. ''Before Sadat said, 'you are my sons, and I am your father.' They (the assassins) said to him, 'No, you are not our father.' So now Hosni Mubarak is tough.''